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Simulation and/or Optimization

We often deal with a number of questions around the use of simulation and optimization tools for problem solving & analysis. On this page, we provide background information that will (hopefully) allow people to better decide where these tools should fit in their problem solving process.

What does the Solution Space look like:

• Problem solvers and analysts use the term "Solutions Space" to describe the graphical relationship between the inputs (levers) they experiment with in their analysis and the outputs (results) achieved.
• Originally, people thought of the solution space as being linear.
• With time, our thinking evolved to understand that the solution space is non-linear.

• With more time, our thinking evolved to understand that the solutions space is not just non-linear, but actually has multiple "local optimals".

• Add to that, the understanding that the solution space is not two dimensional. There are numerous factors (operational levers) that impact output, resulting in a multi-dimensional solution space. Picture the solution space as a "Mountain Range" (pretty intimidating to think of it that way).

Reasonable Expectations of the Solution Space

• With any kind of analysis, you can never know the "Optimal" optimal solution, we can only discover (through analysis or experience) a number of "local" optimal solutions.
• Second, Narrow this list of operational levers to a manageable number. This is optimally two to three (at most five) levers.
• The number of "local" optimal solutions we discover is limited by our perception of reality, and our understanding of the operational levers (dimensions) impacting the solution space

Solution Space Challenges

1. To identify which of the "controllable" operational levers (solution space dimensions) have the greatest impact on operational performance (output).
2. Narrow this list of operational levers to a manageable number. This is optimally two to three (at most five) levers.
3. Experiment with this manageable number of levers to identify the "Best Practical" solution.

Solution Space Strategy

1. If cost effective, first simulate the operations to understand process behavioral patterns, so as to identify Best Practical Solution(s).
2. If cost effective, follow up the simulation with an optimization-based analysis, so as to identify as many Local Optimals as possible
3. Repeat steps one and two, going back and forth between simulation and optimization, as need, budget, and time allow

Note: when I use the term "simulation", I am talking about what would be considered a "statistically accurate" simulation. This implies that you:

1. Utilize input Distributions
2. Run the simulation model for multiple replications
3. Eliminate non-steady state statistics from the output results
4. Develop Confidence Intervals for all critical output statistics.